If you click long on the little green circle in the top left of your program/app start the split screen and can usually choose a second window of the same program/app or the window of any app on that virtual desktop for the other half and afterwards drag the separation in the middle with a long holding click on it to the left and right.
If you use a non retina 13 inch MacBook, some apps can't be placed next to each other due to maximum pixel count limitation of the non-retina screen combined with the minimum width of an app (iTunes minimum screen width is > 50% of a non retina macbook screen size), like iTunes window + Safari window. Two Safari windows can be placed next to another though.
A good workaround is placing the full sized windows of the apps you work with on two different virtual desktops (ctrl + arrow-up-key gets you into the menu) to place them next to each other and switch between the desktops (swipe 3/4 fingers left-right or ctrl + left/right-arrow-key).
Another really great option to me was buying magnet, it's an app that enables shortcuts to place the window on any targeted app in special positions, like left side of the screen filling X% of the screen or right side of the screen with a width of X%.
Those easy shortcuts are cmd + alt + left-arrow/right-arrow-key for example and changeable!
Best regards and I hope you found a good solution or compromise!
Synaikido